Solve (18-10)² + 3³: Combined Square and Cube Number Problem

Order of Operations with Square and Cube Numbers

Solve the following question:

(1810)2+33= (18-10)^2+3^3=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this math problem together!
00:10 First, we calculate inside the parentheses. Always start there.
00:23 Next, let's handle the powers. Remember, exponents come after parentheses.
00:29 Now, let's add the numbers and solve the equation.
00:33 Great job! You've found the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following question:

(1810)2+33= (18-10)^2+3^3=

2

Step-by-step solution

To solve the expression (1810)2+33 (18-10)^2+3^3 , we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

  • Step 1: Parentheses
    First, solve the expression inside the parentheses: 1810 18-10 .
    1810=8 18-10 = 8

  • Step 2: Exponents
    Next, apply the exponents to the numbers:
    (8)2 (8)^2 and 33 3^3 .
    82=64 8^2 = 64
    33=27 3^3 = 27

  • Step 3: Addition
    Finally, add the results of the exponentiations:
    64+27 64 + 27
    64+27=91 64 + 27 = 91

Thus, the final answer is 91 91 .

3

Final Answer

91

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then exponents, then addition/subtraction
  • Technique: Calculate 82=64 8^2 = 64 and 33=27 3^3 = 27 separately first
  • Check: Verify (1810)2+33=64+27=91 (18-10)^2 + 3^3 = 64 + 27 = 91

Common Mistakes

Avoid these frequent errors
  • Adding before calculating exponents
    Don't add 8 + 3 = 11 then square it = 121 + 27 = 148! This ignores the order of operations and produces completely wrong results. Always calculate all exponents before doing addition or subtraction.

Practice Quiz

Test your knowledge with interactive questions

Solve the following problem:

\( 187\times(8-5)= \)

FAQ

Everything you need to know about this question

Why can't I just work from left to right?

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Mathematics has a specific order of operations (PEMDAS) that ensures everyone gets the same answer. Working left to right ignores exponents and gives wrong results!

What's the difference between 8² and 3³?

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82 8^2 means 8 × 8 = 64 (square), while 33 3^3 means 3 × 3 × 3 = 27 (cube). The small number tells you how many times to multiply!

Do I need to show every step?

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Yes! Always show: (1) Parentheses calculation, (2) Each exponent separately, (3) Final addition. This helps you avoid mistakes and shows your thinking clearly.

What if I forget PEMDAS during a test?

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Remember: Please Excuse My Dear Aunt Sally! Or think: parentheses are like containers that must be opened first, then exponents are the most powerful operations.

Can I use a calculator for the exponents?

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Yes, but make sure you know how! For 33 3^3 , you might press 3, then the exponent button (^), then 3. Practice with simple examples first.

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